Doing the Math

[wanders]

OK, I've been working on FEMM 4.2 models for a Halbach array, and I'm having very little luck. In particular, for N40 Neo material that is 1/4" thick, with an air gap of 1/4", with a left-right-up-down magnet sequence and square magnet cross-section, I'm not seeing the field magnitude that I expected. Less than 0.7 tesla, on average across an orthogonal pole pair. Considerably less if you average over the entire Halbach array. See image.

So, what gives? I expected closer to 1 tesla. KF, two questions:

1) How did you get your Halbach array model to generate larger fields? Is my 1/4" material too thin?

2) Where did you get your N42 neo material model? Since N42 is very common, can you upload the parameters needed to model this material? My FEMM 4.2 only came with an N40 material model...

Thanks in advance,

wanders

[Kingfish]

Wanders, this is how I created my model:

Modeling in FEMM Part 1

• I own AutoCAD (ACAD), old version but still works. You could also use Illustrator or anything else that can create an accurate drawing. My ACAD can export in different flavors of DXF so I pick the 97’ version being the simplest.
• Key to creating your model is that it must represent exactly how you are going to fabricate it; make it real-world geometry. With that, all Halbach arrays have touching faces, meaning Left-Top-Right-Bottom (LTRB) repeated over and over with touching faces.
• The air gap is between the stator windings and the magnet faces perpendicular to the LTRB.
  Then I draw a box around the whole arrangement – and this is to enclose the Air material. Take a look at the image below.

• Some of my lines overlap, though I assure you they are all completely enclosed individual boxes. Blue represent Aluminum 7075; I can give you the specs on that in a moment because it is not a stock material in FEMM. Red represents Magnets; let’s not get lost in the size or widths right now. Yellow denotes the windings.
• This particular arrangement is what I call a 3R2S, or 3-Rotor 2-Stator layout. The white box encloses the whole magnetic circuit.
  Export the drawing into DXF. If you are using a different editor, export it into something that FEMM can read/import. Now I am going to start up FEMM and give you the exact instructions on how to set this model up.

FEMM:
Your startup may be different than mine as I have preferences set. Mine is set to begin empty; no preloader.

1. Go to File|New and select Magnetics Problem|OK.
2. Go to File|Import DXF and browse for your recently-saved DXF file, select Open, accept the default tolerance by selecting OK.
3. Go to View|Natural to zoom the model so it maps to the largest X or Y dimension fitting the drawing space; you should easily see the entire model bounded by the Box.
4. Go to Problem and set the units to map to your model; I use MM so I have to change my Length Units to read Millimeters. Set the Depth to map to the length of the magnets. In other words, I have a 20 mm long magnet with a width and height of 5 mm. So the model should represent a bunch of 5mm x 5mm squares and the Depth then becomes the 20 mm length. Make sense? We don’t need to fuss with the Frequency until we start goofing with the windings. Let’s table the windings discussion for now and focus on the magnets problem. Select OK; we are done with this part.
5. Select Properties|Materials Library. This interface was not well-documented IMO, but here you go… You NEED the Air material and it is the first one we can find without looking. Mouse-down on the Air material, drag it over to the right side where it says Model Materials and drop it. Now you have a copy of the Air material in your model. Simple. Follow me as I add more…
   
   1. Left side, open the PM Materials folder, and open the NdFeB Magnets folder. There should be 5 default materials here. You can modify these later but for now let’s pick NdFeB 40 MGOe and drag it over to the Model Materials.
   2. Left side, open the Solid Non-Magnetic Conductors. I made a custom material here. Let’s make one now:
   3. Select a material in the folder – doesn’t matter which one. Right-mouse-click it and select Add New Material, and there instantly is “New Material”. Double-click the New Material to see the Block Property panel. We are going to create a profile for Aluminum 7075; you may or not use this in the future – although it figures large in mine. With the Block Property panel, set the following properties:
      
      Name: Aluminum 7075
      B-H Curve: Linear B-H Relationship
      Relative ux: 1
      Relative uy: 1
      hx, deg: 0
      hy, deg: 0
      Hc, A/m: 0
      MS/m: 20.88
      J,MA/m^2:0
      Special Attributes: Not laminated or stranded
      Select OK, and your new Aluminum 7075 material is ready for use. Please drag and drop that over to the right side as well.
   We are not calculating the windings right now, but if we did, I’d either select Copper AWG Magnet Wire or the Copper Metric Magnet Wire and the appropriate diameter for a single wind and add that to the Model Materials. But we’re not doing that right now; maybe later. Daylight’s burning and there’s fish to fry!
6. Now we have Air, magnets, and Aluminum – this is all that is required to create the model. Select OK to close the Materials Library popup.

Part 2 in a moment, KF

[Kingfish]

Modeling in FEMM Part 2

Adding Materials to Blocks

1. Go to Operation and select Block.
2. Start dropping Blocks into all the individual boxes within the bounding box, and including the inside of the bounding box. It should look like this when finished, with a bunch of <None> designations.
   
   
   
3. Let’s go set the properties. The first one is at the top in the bounding box: Right-mouse-click it so it turns the color RED. Now select the Spacebar; this brings up the Properties for selected block popup. Select the Block type drop-down and change it from <None> to Air, and select OK. Now that area is designated as Air. Simple. Let’s do this now for the Aluminum bits.
4. Right-mouse-click the left and right plates, and every other block down the center rotor beginning at the top; be sure to skip over the adjoining block. Now we have a bunch of red highlighted boxes, yes? Tap the Spacebar to set them all at the same time: Block type = Aluminum 7075, select OK, and you are done.
5. The Halbach Array is trickier but it too can be done en masse – you just have to set them in 4ths:
   
   1. Using the image I provided, the magnets will face Top (90*), Right (0*), Bottom (270*), and Left (180*); keep this in your head and I do these next batches.
   2. Select the 6 Right-facing magnets, Spacebar, Block type = NdFeB 40 MGOe, and Magnetization Direction = 0 (default), and select OK. Repeat for the next 3 Left-facing, except the Magnetization direction = 180*.
   3. Select the 4 Top-facing magnets and set the direction to 90*, and repeat for the 4 Bottom-facing with the direction set to 270*.
   My diagram has two sets of windings and I am going to set the material but not complete the rest of it because that is a different conversation.
6. Save the Model: File|Save (give it a name).
7. Now we are ready to evaluate the model. Select Analysis|Analyze; there should be a popup that runs a little status bar then disappears after a brief moment – depending on how quickly your computer processes math. Select Analysis|View Results and you get a new tab with a force representation. Not terribly meaningful.
8. Just below the Plot X-Y menu is a button that has four colors in a diagonal direction and select it (or select View|Density Plot) to bring up the Dialog popup. Check the Show Density Plot box and select OK. It should look precisely like the image below.
   
   

Part 3 uno momento por favor, KF

[Kingfish]

Modeling in FEMM Part 3

Measuring
I kinda cheat and not do it right because the instructions are not precisely clear to me. However – let me show you the lazy inaccurate method that is definitely not the proper way – and if BTW you should learn the proper way I expect you to tell me so I can remove my dunce cap and myself from the Fool’s Corner and enjoin with you over a beer in celebration at the enlightenment. But first – the cheat:

1. Look at the menu bar; just below the Zoom menu is a menu box with a two tiny black boxes connected by a red segment. Select that box. Now clock between two points across the air gap between the left HA and center magnet (Non-HA) so it draws a red segment across; it should look like this:
   
   
   
2. From the top menu, select Inegrate|B.n (default) and OK which displays the Integral Result.

Before we continue, let me share with you the details of my model used for these diagrams:

• The Left & Right Aluminum plates are 4.8mm thick.
• The Magnet Height = 8mm
• The middle rotor magnet height is also 8mm.
• The air gap between the magnetic faces is 5mm.
• The average air gap of the bounding box is 10mm (not terribly important, but don’t make it less).

Back to the Results, my B.n value is 0.880244 Tesla. That’s pretty rocking for wimpy magnets; however I don’t think I can afford the cost per wheel to make this design. It’s nice to dream though. Also, you can also select the Plot X-Y and get some interesting results of value across the gap. The FEMM Help Topics go into more details on what the other measurements mean and how to make them.

Rereading your request, Biff forwarded to me more FEMM materials here on this thread:
Material Library in FEMM

Hopefully this is enough to spur you on your way.

Happy Modeling, KF

[wanders]

Hopefully this is enough to spur you on your way.

KF, you never cease to amaze! Thanks for the extensive FEMM tutorial. I had figured out most of this stuff (FEMM excels in neither step-by-step documentation nor user-interface niceties), but it is really useful to have this vast tutorial in a single place.

BTW, if the copper depicted in your drawing are the "into the plane" and "out of the plane" currents of a single phase coil of a (dual) stator, you will almost certainly want to make the coils twice as large in the theta direction (unless there is something I really don't understand about Halbach-array motors). I'm sure you can get your motor to run as depicted, but it may be more efficient with larger coils.

ALSO, regarding getting the average normal B field on a contour, your "cheating" method suffices, but the simple way to get an exact contour directly (say, through one-half magnet phase directly in the center of the gap) is by putting in points (but not lines) before the mesh generation step. I find that the mesh generated can be different, based on where the points are. Anyway, after analysis, the points are still there, and can be used to generate an integration (actually, averaging) contour. If you are using a grid, make sure the grid spacing is no greater than half the air gap distance. Easy!

Thanks again!

wanders

[Kingfish]

Wanders you are most welcomed friend.

Those are truly choice words. I drew many models and really didn’t give a hoot so much about the coils other than curiosity because the magnetic model had preference. You are correct: Placing two points in the middle where it can bisect the windings is the correct way to do it; I was in a hurry and couldn’t be bothered hence the cheater method.

Eric has suggested the proper way to get a good model is to rotate the windings through the magnetic flux and take many readings to develop the actual theoretical analysis – but that’s a lot of work when I just want to try various physical geometries, multiple rotors, air gaps, and materials for simple edification. Imagine that I have another series of unpublished models and results using a Flux Ring. The conclusion was: Use the Halbach to reduce the complexity and increase the density up to 10-15% more.

Now I am on the Litz Wire hunt, although paused for the moment as I take care of immediate winterizing needs. Much left to do though.

And – we need sinusoidal controllers to take us there once we build these wheels, right?!

<hint hint> KF

[wanders]

And – we need sinusoidal controllers to take us there once we build these wheels, right?!

<hint hint>

Maybe. It certainly would make the motor operation quieter. I read an interesting white paper from PMD (who makes motor controller chips and other things). They have a technique called field-oriented control that looks interesting. PMD claim that it has all the advantages of sinusoidal control with less complexity and control loop error. They make some compelling points, but of course they are promoting their products ...

Regarding Litz wire, the best resource I've seen is MWS WIre Industries.

wanders

[Kingfish]

MWS: Yeah, I have those folks high on my contact list for New Year;
Re: Is all magnet wire the same?

Patiently waiting. KF

[Kingfish]

Modeling in FEMM Part 4

Development of Winding Circuits and calculating Power Output
Now that we have a model with magnets, let us add the windings and circuitry to complete the full model.



In the image above we have four tiny boxes that represent the windings in section. We are going to define these as follows:

1. From the top menu, select Properties|Materials Library. Add a copper winding material. I work in metric units, so I will select Copper Metric Magnet Wire|2.5mm and drag-drop it over into the Model Materials section. Select OK to close the box. Note: I just picked 2.5mm for example; it is worth exploring Litz wire (although you will need to create custom material to do so).
2. Select Properties|Circuits|Add Property:
3. Set Name = “i” without quotes. (The name can be whatever you want).
4. Leave the circuit set to Series if your windings are in series.
5. Set the ‘Circuit Current Amps’ equal to the value that you think will be the operational Phase Current. As a rule this should not exceed √3 * Battery Current Limit (and we sure hope it is a lot less). Select OK, and OK again to close the boxes.
6. Select Operation|Block (or pick the ‘Circle around the Node’ button), and then Right-mouse-click the Blocks inside the top two windings so they turn red. Hit the Space Bar:
   
   1. Set the Block type = 2.5mm
   2. Uncheck ‘Let Triangle choose Mesh Size’ & set Mesh size = 1.
   3. Change ‘In Circuit’ to “i” (or whatever you named it).
   4. Set ‘Number of Turns’ to the value that you need (providing they fit).
   5. Select OK to close the box.
7. Repeat these steps for the lower windings with one change:
   
   Set ‘Number of Turns’ to the NEGATIVE value that you need. This indicates to FEMM that the current flows in the opposite direction. If you do not set this to a negative number FEMM will not produce useable answers.

Now we are ready to make several important measurements.

1. Select Problem. Insure the Frequency is set to ZERO (0). Select OK to close the box.
2. Select Analysis|Analyze (goes off and computes), then Analysis|View Results.
3. Select Operation|Contours and draw a diagonal line across the void of the top-left winding in a manner similarly displayed in the image below.
   
   
   
4. Select View|Circuit Props and note the results; they are selectable, so copy and paste them into Notepad or Spreadsheet; it’s interesting stuff and we’ll want this for reference in a bit. Just note that these are the values at ZERO rotation.
5. Select Integrate|B.n to note the Integral Result; again the values are selectable. This is your best average Tesla (at least as best as we can model).
6. Select Operation|Areas (or the ‘Green box bounded by four points’ button) and click the center of the four winding cross-sections to fill them in a manner similar to below:
   
   
   
   Note: FEMM has a quirky bug and freaks-out occasionally when trying to do this when the color option is plotted out and will flood the whole model in green. Just avoid plotting color when doing this measurement.
7. Select Integrate|Lorentz force (J x B) and note the y-component given in Newtons. We need this value to meet or exceed the total required Force previously determined at the beginning of the Thread.

Let’s say for the sake of argument that I require 450 N to spin this wheel at 30 mph. Let’s say I have 20 pole-pairs. The relationship of the y-component is as follows:

Total Force = (y-component) * (√3) * (20 pole-pairs). Working backwards...

450 N / (√3) * (20 pole-pairs) ≈ 13 N.

If the value of the y-component is less than this value then I need to go tweak the model. If the value is higher than required then we get to eat ice cream. If the value is really high then perhaps we need to scale back and reign in the costs of materials. Regardless, this particular measurement is very important.

Other measurements can be useful and I encourage exploration. OK, so now let’s figure out what the results are for when this wheel is spinning at 30 mph.

1. Switch back to the FEMM Model
2. Select Problem, and this time we set the Frequency = 112; in my model 112 Hz = 30 mph. Select OK to close.
3. Select Analysis|Analyze (goes off and computes), then Analysis|View Results.

Notice how the flux lines change. If you want to see it in color, select View|Density Plot and check ‘Show Density Plot’ and select OK to close the box. Makes for a pretty picture. I tend to leave the color step out when developing a solution to speed up my process, however it is quite fun to view the output.

Once again select View|Circuit Props and note the difference between the values when the Frequency was set to Zero and when set to 112 Hz. I am particularly interested in Real Power; the lower this number is the more efficient the design. To calculate the total power used using the same example figures, let’s say I measured Real Power to be 35 Watts:

Total Power = (Real Power) * (√3) * (20 pole-pairs) =>

35 * √3 * 20 = 1212.4 W

Not bad, could be better; we want it better! Other measurements can be taken, and I encourage exploration.

That’s what I knows for this evening. Hope it helps.
Happy Modeling, KF

[Kingfish]

Modeling in FEMM Part 5
Using LAU Scripts

In this segment we will analyze how to use a bit of automation to develop a clearer picture of model performance. There is a bit of a challenge for AF motors on how to do this correctly. I wanted to develop a baseline first and try to compare an AF hub motor to a known RF hub motor. Presently I use the 9C 2806 on my ebike as I am quite familiar with how it operates. The complete investigation of the 9C 2806 hub motor in FEMM has come to a safe conclusion, at least to the point where one can understand the nature of the motor well enough, and ending with a nice example of Lua scripting.

What I’d like to do now is adapt those scripts for use with AF. The first step towards that direction is to develop a new AF model for study. I chose a geometry that I think is fun, commonly available, and although perhaps not entirely practical for a hub motor, it is compact enough that it was easy to configure.


AF model using common Windmill magnets

AF_Magnetics_Windmill.zip

Includes FEMM model, and modified Lua scripts for AF.

(7.66 KiB) Downloaded 52 times

Details:

• Windmill Magnets: 16p N42 (model uses N45) 8” OD x 4” ID x ¼” thick, 2-Rotors (hub covers); inexpensive and easy to acquire. Link
• Windings: 18t of 1x4 Type-8 Litz (~12 AWG-equivalent) x 6 turns per winding. Link
• Coreless. (The model uses Air, but could be a host of non-magnetic materials).
• Back iron is pure iron, 4 mm thick. In the real world this might be Stainless Steel 340.

This model was drawn up and a section was taken at the 76 mm radius (about ½ magnet length). Note that there are a couple of extra poles on the right; we need that for the scripts which will be explained forthwith.

With Radial Flux hub motors we rotate the magnets and back iron relative to the stator. For AF, the motor is unraveled and looks like a racetrack; I think to think of it as a maglev rocket sled track. And instead of rotating magnets, we translate the windings laterally – hence the reason why we need an extra pair of two at the end of the series.

Scripts Examined:
The credit for these scripts rightly belongs to Biff who was kind enough to give us a hand on the 9C 2806 studies. I took the liberty of studying them and making a couple of adjustments which I’d like to explain in detail if folks would be keen on that.

Two LAU references are the FEMM Help (very abbreviated), and online – though I have to say that I found it difficult to find a consolidated resource. That said, this link is pretty fun to explore: http://luatut.com/. Don’t be afraid of Lua; it reminds me of Jscript in a way.

The big changes to Biff’s scripts were resetting the poles to the correct amount (natch), and adding variables and maths that would determine the dX translation. With the Windmill model, these values are:

• rotor_poles = 16;
• rotor_radius=76; (in mm)
• dX = 0;
• dX_per_step = (rotor_radius*rotor_angle_per_step*3.1416)/180;

FEMM has a feature where you can group objects together for study. This is the part about FEMM that is goofy: If I assign a volume to have a property then I expect that volume to inherit all the traits. No so in FEMM: We have to do double-duty to get our model correct (and I have already done the diligence with the attached model). To modify a new model, briefly:

1. In FEMM, go to Operation|Segment, click the windowing button, and box the whole model sans the bounding box, and group them as “2”.
2. Redo the operation for just the windings and group them as “1”.
3. Now add the nodes for the magnets, and then for windings. Select Operation|Block, then the windowing button and select all the winding nodes. Here I set them all to the same value in one swing: Material, Circuit (default to A), Turns (I set them to “-6”), and Group = “1”. Individual processing will now go faster.
4. Repeat for the Magnets, setting Material, Direction (I picked “270”) and Group = “2”. Then I go back and individually reset every other pair’s direction to “90”.

Anyway – that’s the trick to getting the nodes AND the segments to move together, and it needs doing for either RF or AF models.

Now, back to Lua:

• With RF, the group selection command is mi_selectgroup(2) which equals the magnets and back iron. I kept that representation in AF, and used Group 1 for the windings. With the AF scripts this changes to mi_selectgroup(1).
• For RF, the model rotates the selected magnets and back iron with this command: mi_moverotate(0, 0, rotor_angle_per_step, 4). However with AF, we want to translate across the X-Axis, so I changed it to: mi_movetranslate(dX,0,4);
• RF then increments with: rotor_angle = rotor_angle + rotor_angle_per_step, whereas AF increments with: dX = dX_per_step;

Broken down into bits, it’s pretty simple to comprehend.

The variable-torque-AF_Windmill.lua script just ramps the current up from 10 to 110. I think that for the most optimum result the windings need to be in proper alignment with the magnets – and here I am at a loss but to guess that the running-torque-AF_Windmill.lua script would provide the clue.

Torque:
There is one other change I made to new-flux and running-torque scripts for AF...

RF torque is determined around the X,Y point of 0,0, and the command that is called is: torque = mo_blockintegral(22) which is the “Steady-state weighted stress tensor torque”. However, because of the geometry of our model we do not have a radius per se. Instead I measured mo_blockintegral(11) which is the “x (or r) part of steady-state Lorentz force”. This is at least consistent with my previous AF FEMM modeling. It still needs a bit of help to convert that to an apples-to-apples value so that we can realistically compare the RF and AF models.

By definition, Torque (Ï„) = Radius (r) X F, or
τ = rFsin Θ

If this is correct then it should be a simple matter of modifying the script to provide a suitable output.

Biff, chime in anytime friend

Methodically, KF

[Biff]

Looks good Mr. The King.

The point about producing optimal torque is right, but wrong at the same time. If you find the place which gives you optimal toruqe, then run your variable-torque script at that location, you will produce optimistic results. I tend to be a pessimist, picking a random point, or one that you know is a good average torque point is probably a good place to run the scripe, espically if you find there is a large torque ripple in the design (that should become obvious in the running-torque simulation).

Also try mo_blockintegral(18) (weighted stress tensor force) I have found that to be more useful than the the lorentz force, but that could be because all of my simulations include force or torque caused by magnetic attraction, not just current induced force.

I have downloaded your model and scripts, and might get a chance to look at them during a layover tomorrow, otherwise expect some more feedback Monday or Tuesday night.

In the mean time, I'll give you some homework. Figure out how long the copper will be in each phase, and what the resistance will be in a phase winding at 80degrees celcius. Then estimate how much heat you can actually extract from your stator, and determine how much RMS current it will take to produce that heat, and finally use your simulated results to determine how much torque you will get at that current. That is really the biggest limiting factor to a motor design; determining how much current you realistically expect to be able to put through the coils.

-ryan

[Biff]

I had a quick look at the model.

It is a good idea to create some magnets at each end of the simulation that don't interact with the coils, to reduce the effects of "linearizing" your motor, it will simulate a continuous magnetic field like what woudl be seen by the coils when wraped into a circle.

Also you won't want to use Stainless steel for back iron as it is non-magnetic.

-ryan

[Biff]

Sorry for all the short reples, I just have time between flights to get a little bit of stuff done and I don't want to forget about it.

In the back iron, you want around 2T max flux dencity .. the 2.4 you have right now will most likely cause a force limitation as you increase the current in the coils. For most motor design the rotor yoke flux dencity is kept at 1.8-1.9T when laminated, so going to solid will allow you to push that a bit because you don't have to worry about the space taken up by insulation between laminations.

-ryan

[Biff]

The thin back iron doesnt seem to cause any problems with torque, the Kf remains constant past 100A RMS / phase. Also with the coreless axial flux motor, the torque shouldn't change significantly through the cycle, so wherever you test the Kf (aka Kt once converted to a radial motor) should be fine, so ignore what I said earlier. The phases as they are in your design are Phase A = -180, B=-60, C = 60 (or close to that). The (DC) Kv I get is around 46rpm/V delta and 28RPM/V Wye. The Kf = 5.36N / (Amp RMS/phase). I havent checked to see if that Kv and Kf match up when converting between electrical and mechanical power. I did find that Lorentz force which you suggested works better than Stress Tensor Force.

Is there any reason why you didnt fill the stator with copper? are you planning on building some sort of support structure for the coils or something? I quickly ran a simulation where the windings would be similar to that of the CSIRO motor completely filling the airgap, and the Kv came down slighty (suggesting more torque for the same current), from the same magnets and numbers of turns, it also increased the crossection of copper, which would reduce your copper losses.

-ryan

[Kingfish]

Hiya Biff

Copper fill
I ran several simulations that did show marked improvement when the windings were filled to their maximum, however I am not convinced that the stator could be constructed having any rigidity without some sort of support. For that I allowed 2mm between the windings to provide ribbing, and likely a perimeter band as well. I haven’t decided if the sides facing the magnets will have a thin facing sheet as well: Everything depends upon flatness, and maintaining that flatness during some very high lateral forces. Not having built one before I tend to err on the conservative. The losses are visibly noted in the graphs below.


Front view of the AF Windmill magnet and winding layout (note the gaps between magnets and windings).

Back iron
I ran through several iterations with various materials and back iron thicknesses from the exotic to the absurd. Getting T < 2 had the thickness up to 8mm ≈ 5/32 inch which might be realistic if they were ½-inch thick magnets, however they’re only ¼-inch. It probably deserves some investigation to comprehend the limits for modeling. To be honest it made me go back and review Halbach arrays in like configuration, but I was hating it because of the projected costs and small drop in total Force.

Hell crazy on Lua
I do have some graphs to post though. Read, tweaked, read some more, tweaked some more – applied the same scripts to both the 9C 2806 RF and the 16p18t AF (with obvious customizations) and… it just begs for more questions. There’s even a Halbach version of the 16p18t… Biggest change was that I included the Force and the Torque for a full 2-pole cycle. The Force is calculated using the mo_blockintegral(18) method.

AF 16p18t @ 10 Amps


Measuring Torque is kinda pointless with AF.

High/Low/Diff Force = 105/-5/111 N
Ave Torque = 53.4 Nm

AF 16p18t Halbach @ 10 Amps



High/Low/Diff Force = -78/-3/75 N
Apologies; I think this motor is running backwards.

9C 2806 @ 10 Amps


For comparison...

High/Low/Diff Force = 35/-37/72 N
Ave Torque = 11.3 Nm

Modified LUA script outputs both Force and Torque side-by-side for easier comparison.

running-force.torque.zip

(1.1 KiB) Downloaded 58 times

The changes to the AF scripts were simple and could have both the force and torque combined, but I woz lzy. The basic problem with Torque calcs on AF is that they revolve around 0,0 so it’s kinda pointless. The script below calcs the force for the Windmill through two magnet/one complete magnetic pole, with nice headers for Excel.

running-Force-AF_Windmill.zip

(1.25 KiB) Downloaded 92 times

I do want to review the maximum Tesla that can be crammed through a thin back iron; that is key to factoring out design and manufacturing. I wonder what the permeability of CRS is.

Twiddlin’ KF

[Biff]

Hiya Biff

Copper fill
I ran several simulations that did show marked improvement when the windings were filled to their maximum, however I am not convinced that the stator could be constructed having any rigidity without some sort of support. For that I allowed 2mm between the windings to provide ribbing, and likely a perimeter band as well. I haven’t decided if the sides facing the magnets will have a thin facing sheet as well: Everything depends upon flatness, and maintaining that flatness during some very high lateral forces. Not having built one before I tend to err on the conservative. The losses are visibly noted in the graphs below.

Yep, stiffness is a big issue with the CSIRO motor. Once those winings get warm, the stator turns to jelly, bends, makes contact with the rotor (there is a 2mm airgap beween the stator and the rotor) then you are screwed. It is a good idea to have a support structure to the system, it might help you get a bit of the heat out as well.

Hell crazy on Lua
I do have some graphs to post though. Read, tweaked, read some more, tweaked some more – applied the same scripts to both the 9C 2806 RF and the 16p18t AF (with obvious customizations) and… it just begs for more questions. There’s even a Halbach version of the 16p18t… Biggest change was that I included the Force and the Torque for a full 2-pole cycle. The Force is calculated using the mo_blockintegral(18) method.

I found that Lorentz force blockintegral(11) which you initally suggested, provided more expected results for force. I'll have a look at your scripts and post some more feedback.

I do want to review the maximum Tesla that can be crammed through a thin back iron; that is key to factoring out design and manufacturing. I wonder what the permeability of CRS is.

Twiddlin’ KF

What is CRS? Permiabilty and saturation are similar but not related. Pure iron saturates at around 2.2T Laminated Iron at around 2T, Laminated Cobalt at around 2.3T. For high permiability you want Nickle. For Nickle see Mu Metal for an extreme example http://en.wikipedia.org/wiki/Mu-metal, or Carpenter "49" for something you can get in laminations, but you will notice that Carpenter 49, saturates at around 1T

http://cartech.ides.com/ImageDisplay.as ... m+thick%29

from the rotor spec link here: http://cartech.ides.com/datasheet.aspx? ... &c=TechArt

Carpenter Hyperco50 (cobalt alloy) is high saturation 2.4T , http://www.cartech.com/ssalloysprod.aspx?id=2360

From the simulations, I don't think the high flux dencity of the back iron is going to cause a significant problem for this motor like I initally thought. I haven't studied the simulations extremely closely, so I could still fall on either side of the fence for this decision.

-ryan

[Biff]

I confirmed that mo_blockintegral(18) doesnt' work for your application. mo_blockintegral (11) provides nice results (see attached image)

The Force at 10A RMS per phase is 54.4N with a ripple of about +-0.9N, so that is pretty smooth. Using the 76mm radius, that puts the torque at 4.1Nm.

At 1000 RPM, that translates to about 430W of power (1000 * pi / 30 * 4.1)

And that agrees with my previous statement of DC Kv of 46 RPM / Volt, which translates to 14.7V RMS per phase at 1000 RPM. 14.7 V * 10 A * 3 phases = 440W.

So both Electrial power, and mechanical power match up pretty close, which suggests that the simulation and analysis is accurate.

Have you figured out what the resistance of each phase it yet? how much power is going to be produced in the coils (I^2 * R) by the 10A RMS per phase?

-ryan

[Biff]

I forgot to mention, in the script, if you want to simulate more than 1/2 of an AC cycle, you can just change the phases_to_simulate variable from 0.5 to 1 or 2 or whatever rather than multiplying steps in the for loop. Also if you want to have smaller displacement between steps, increase the steps variable (right now in your simulation you have it set to 15, I put it at 15 because your first models took so long to solve, but now they are good and fast so you can do many more steps in the same amount of time). For analyzing the flux linkage and turning that into a BEMF I usually put it at something between 40 and 50 steps and 1/2 cycle. When computing cogging torque, I do 90 steps in 1/8 of a cycle.

-ryan

[Kingfish]

Hi Ryan

I'm on travel and can't get to my files for a few days. However I did want to ask kindly why you thought Lorentz (11) was better than Force (18). Just curious

CRS = Cold Rolled Steel. It is very common and sturdy. Requires painting or plating to prevent corrosion. The only Nickel alloy I considered was Stainless Steel (SST) 340 which is magnetic, strong enough, and modestly resistant to corrosion.

Stator: The inside of the coils could be aluminum 6061 or 70XX series, and have a thin carbon-fiber or fiberglass sheeting epoxied to each face, pressed and heat-cured. The ribbing would have to be integrated to the central hub interface, possibly water-jet cut from one plate.

I hope to get back to my studies this weekend

Cheers from abroad, KF

[phyllis]

what, alu inside the coils?

Also, what lateral forces is it that was mentioned on the stator?

[Biff]

what, alu inside the coils?

Also, what lateral forces is it that was mentioned on the stator?

I think he means that the hub, supporting the coils , not actually inside the coils is to be made of aluminum. Obviouly any (non-laminated) aluminum that is in the magnetic field of the rotor would cause significant eddy current loss.

Hi Ryan

I'm on travel and can't get to my files for a few days. However I did want to ask kindly why you thought Lorentz (11) was better than Force (18). Just curious

I'm not exactly sure, I havent' give it much though, because Lorentz just seemed to work. I think it has more to do with the loose meshing than anythign else, but the force while moving that you were finding seemed to have very large errors.

[Kingfish]

Plan-E eMoto AF DD Hub

It’s been a while since I posted on this thread and much has changed. Namely I completed a significant personal goal of riding my present eBike (P1 as 2WD) to California and back. This experience taught me a lot about how I want to use my next EV experiment, and I think I can quantifiably say without hesitation that next year I want to travel in the lane with all the rights and responsibility of a motorcycle. For the amount of time and energy I am spending to potentially create an AF motor, I just think it makes economic sense to go for it and produce an eMoto (I like that phrase) AF DD hub instead of an eBike version.

For one, I can discard the 200mm diameter limitation of trying to match a 9C-like physicality and attempting to mount it as a front hub on a DH 20mm-axle fork: All of that business of trying to stuff 10 lbs. into a 5-lbs sock is gone. We can start from a clean slate, and build with what we already learned.

Challenges:
This is actually a bigger leap than crafting a new bicycle; it will cost a lot more to acquire, manufacture, and assemble parts to complete a simplistic hub for testing.

• Define the parameters of operation
• Design a basic motor (Alpha)
• Build a dyno (thread already started)
• Acquire the appropriate equipment for repetitive measurement
• Evaluate a base to test against (9C cos I have several)
• Test and Perfect methods of assembly before committing to the 2nd-phase (Beta)
• Then build a motorbike framework to support the final application.

I am going to start with the Plan-D model and change it accordingly to match the new specifications. The final bike will still utilize 2WD; I am totally happy with the utility for a number of reasons:

• Redundancy (insurance)
• Traction (safety)
• Acceleration (thrill!)
• Scalability (power)

Targets are:

• Match the output of a 250cc motorcycle; about 24-28 hp, or 9-11 kW per wheel
• Hold 75 mph at STP on level ground continuously for hours
• Run efficiently; don’t be a power-hog
• Run cool; presume there is some sort of active cooling both for the hub and the controller
• Ease of Assembly

I will post the specs and math in a bit; I’m still putting together initial estimate and calculations, but it won’t be long.

Cheers, KF
PS - It is with hope that MRVass will run the MySQL scripts I provided so the corrupted characters will be fixed – making this entire thread much easier to read.

[Kingfish]

Initial changes between Plan-D and Plan-E:

• Wheel is motorcycle, 110/70-17 (Front) & 130/70-17 (Rear). Doing the Math, it turns out they are about 24.1 inches in diameter when taking into account the tyre dimensions. This is nearly identical to Plan-D. However we are no longer constrained by factors of bicycles and can use most of the spoke length to our tremendous advantage.
  
  
  Was: r = 90mm, or 0.090m
  Is now: r = 152.4mm, or 0.1524m
• Horsepower has dramatically increased from 2, now up to 14.
• Target Velocity has increased from 30 mph to 75 mph / 121 kmh.
• Magnets are off-the-shelf at 0.75x1.5x.025 inches (19.05x38.1x6.35 mm) and available in a robust temperature range.
• Poles and Teeth are the same: 32P (16:1), 30T (10T/phase)
• Force and Torque have naturally changed; let’s Do the Math!

Calculate Rotation

Given Wheel Diameter (d) = 24.1 inches/ 0.61214m
Circumference (C) = πd = 75.712 inches/ 1.9231m
fps = (mph * 5280)/(60min * 60s) => (75 * 5280)/3600 = 110 fps or 33.528m/s
rps = (110 fps * 12 ipf)/(75.712 inches) = 17.434 rps
rpm = 17.434 rps * 60 seconds = 1046 rpm

Calculate Torque (τ)

Given: Power (P) (kW) = (τ (Nm) * 2π * rpm)/60000,
τ = (P * 60000) / (2π * rpm)
τ = (11 kW * 60000)/(2π * 1046) = 100.4 Nm

Calculate Angular Velocity (ω)

ω = 2π * rps
ω = 2π * 17.434 = 109.5 rads/s

Check our work

P = τ * ω
P = 100.4 * 109.5 = 10993.8 watts; an error of 0.06%... good enough

Calculate Motor Constant (K)

K = τ/ω
K = 100.4 / 109.5 = 0.91668
Kt = K/3 (3-Phase) = 0.30556

Calculate the Ideal Steady State

P = Current (I) * Voltage (V); solve for V
We already know that V == τ, therefore
V = 100.4 Volts, and I = 109.5 Amps

Solve for the Length of Conductor

Given: F = IL x B, where Force (F) = I * Length (L) x Magnetic Field (B)
L = F/(IxB); Presume B = 0.5 Tesla, also written as L = τ/2rBI
L = 100.4/(2 * (0.61214/2) * 0.5 * 109.5) = 2.995 m

Note: I need to switch to Nm/metric to complete the rest of the calcs. With exception to references wheel diameter and velocity, everything else with be in SI-units.

More in a bit, KF

[Kingfish]

More calcs...

Evaluate Conductor Length over a range of voltages
For this next series, presume that I am going to reuse my mini-mountain of lil’ LiPos, each brick being the 5S1P 5Ah 15/2C Zippy FlightMax. The calculation for I = P / requested V.

• Vbatt = 63; 15S; I = 11000 / 63 = 174.6 Amps (A). Using L = τ/2rBI, L = 1.1789 m
• Vbatt = 84; 20S; I = 130.9, L = 2.096 m
• Vbatt = 105; 25S; I = 104.8, L = 3.275 m
• Vbatt = 126; 30S; I = 87.3, L = 4.715 m

The relationship between current and voltage is interesting, though not precisely linear as we can see from the graph below.



Corrections
At this point we must reduce the value of r because it will never be equal to the radius of the tyre. The rim diameter is 17 inches; therefore I propose that we create an average magnetic diameter of 12 inches:

New r = (12 inches * 0.0254)/2 = 0.1524 m

In addition, the strength of the Magnetic field (B) will be more than 0.5 T; from my experience with FEMM we can presume this value will be > 0.65 T, so let’s pick that – being the optimistic designers of motors et al.

B = 0.65 unless otherwise noted.

Calculate Force

Force (F) is calculated as F = τ/2r
F = 100.4 / (2 * (0.61214/2)) = 329.45 N

Note that the Force required in Plan-D was 377N; now we can appreciate the longer radius!

Recalculate the new Conductor length using 63 Vbatt

Given: L = τ/2rBI
L = 100.4/(2 * 0.1524 * 0.65 * 174.6) = 9.5238 m

Calculate Frequency

Frequency (f) = rps * Number of Pole-Pairs (pp)
32 poles = 16 pp
f = 17.434 * 16 = 278.95 Hz

Calculate the Number of Turns per Tooth
We now have all the pieces of the puzzle to characterize the conductor and determine the number of turns per tooth for this motor. This is a 3-Phase motor, therefore…

Iphase = I/√3 => 174.6/√3 = 100.81 A

This motor has 30 teeth, 10/Phase, therefore…

Itooth = 100.81 / 10 = 10.081 A

Length of Conductor per tooth becomes...

Ltooth = Total L / #pp / # phases => 9.5238 / 16 / 3 = 0.3175 m

Magnet Length = 1.5 inches / 38.1 mm (a figure previously given)

Number of Turns can now be evaluated as...

#Turns = Ltooth / (2 * Magnet Length)
#Turns = 0.3175 m / (2 * 0.0381 m) = 4.2

More... KF

[Kingfish]

Stator Redesign

I spent a good deal of time investigating Magnetic Wire and Litz Wire, and this and that… When yer On the Road for tens of miles it gives a person plenty of time to think about these things, and I have come to the realization that whatever I create – I must adhere to the principle of K.I.S.S.

How do we solve to make the stator dead-simple and solid-state? I take no credit; it belongs to Goethe who proposed early on Page 3 of this thread to use a PCB. The value of this suggestion weighed heavy and the more I pedaled, the more sense it made for a number of reasons:

• Fabrication is automated; remit the design to the manufacturer and in return is a finished product with greatly reduced labor costs.
• Waterproof
• Temperature-tolerant & stable
• Multilayer construction, rigid, stiff
• Thick copper plating can be used to draw heat away if designed appropriately

An example of a PCB-Stator.

Moving right along…

Calculate Trace Width
I used a website provided in another thread called appropriately enough: PCB Trace Width Calculator. The following values were used:

• Trace Current = 10.08 A
• Copper Plate Thickness = 3 oz./ft^2
• Temperature Rise = 10°C
• Trace Length = 0.318 m

Results:

• Internal Trace Width = 6.31 mm (1/4 inch), and external exposed to air = 2.42 mm.
• Power loss = 0.862 w for internal and 2.24 w for external.

From this calculation the trace is hugely phat. We can skinny-up this guy by increasing the copper plating, allowing a temperature rise up to 30°C, accessing the multilayer features by creating parallel traces, and by reducing the current if we elect a higher voltage. So far we’ve been looking at a single stator; we could easily add another stator-rotor pair and split the load. All can be done and are possible.

At this point though we have enough information where modeling in FEMM can begin.

Enjoy, KF